论文信息 - The expected number of random elements to generate a finite abelian group

The expected number of random elements to generate a finite abelian group

Suppose G is a finite abelian group with minimal number of generators r. It is shown that the expected number of elements from G (chosen independently and with the uniform distribution) so that the elements chosen generate G is less than r + where= 2118456563...The constant is explicitly described in terms of the Riemann zeta-function and is best possible.

Carl Pomerance | C. Pomerance

[1] H. Lenstra,et al. Factoring integers with the number field sieve , 1993 .

[2] Alan Williamson,et al. The Probability of Generating the Symmetric Group , 1978 .

[3] Ekkehard Krätzel,et al. Über die Anzahl der abelschen Gruppen gegebener Ordnung , 1994 .

[4] F. V. Atkinson,et al. The Riemann zeta-function , 1950 .

[5] Jacques Stern,et al. Short Proofs of Knowledge for Factoring , 2000, Public Key Cryptography.

[6] William M. Kantor,et al. The probability of generating a finite classical group , 1990 .

[7] H. Lenstra,et al. A rigorous time bound for factoring integers , 1992 .

[8] A. Ivic,et al. The Riemann zeta-function , 1985 .

[9] William M. Kantor,et al. The probability of generating a classical group , 1994 .

[10] Aner Shalev,et al. The probability of generating a finite simple group , 1995 .

[11] Igor Pak,et al. On Probability Of Generating A Finite Group , 1999 .